End Behavior of Polynomials

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

What does a positive leading coefficient indicate about the end behavior of a polynomial?

Back

If the leading coefficient is positive and the degree is even, both ends of the graph rise. If the degree is odd, the left end falls and the right end rises.

Front

What does a negative leading coefficient indicate about the end behavior of a polynomial?

Back

If the leading coefficient is negative and the degree is even, both ends of the graph fall. If the degree is odd, the left end rises and the right end falls.

Front

How does the degree of a polynomial affect its end behavior?

Back

The degree determines whether the ends of the graph rise or fall. Even degrees lead to both ends behaving the same, while odd degrees lead to opposite behaviors.

Front

What is the difference between even and odd degrees in polynomials?

Back

Even degree polynomials have symmetrical end behavior, while odd degree polynomials have opposite end behavior.

Front

What is the end behavior of a polynomial with a positive leading coefficient and an even degree?

Back

Both ends of the graph rise.

Front

What is the end behavior of a polynomial with a negative leading coefficient and an odd degree?

Back

The left end of the graph rises and the right end falls.

Front

What is the end behavior of a polynomial with a positive leading coefficient and an odd degree?

Back

The left end of the graph falls and the right end rises.

Front

What is the end behavior of a polynomial with a negative leading coefficient and an even degree?

Back

Both ends of the graph fall.

Front

How can you determine the leading coefficient from a polynomial expression?

Back

The leading coefficient is the coefficient of the term with the highest degree when the polynomial is written in standard form.